Given that: \(\displaystyle{2}{\cos{{\left({x}+{50}\right)}}}={\sin{{\left({x}+{40}\right)}}}\) Show, without using a calculator, that:

Overath097p

Overath097p

Answered question

2022-03-25

Given that:
2cos(x+50)=sin(x+40)
Show, without using a calculator, that:
tanx=13tan40

Answer & Explanation

SofZookywookeoybd

SofZookywookeoybd

Beginner2022-03-26Added 15 answers

Using the well-known identity
cos(90x)=sinx
since the cosine function is just a 90 horizontal translation of the sine function.
Taking x=40 give us cos50=sin40 and letting x=50 establishes the second result. Then
2coscos502sinxsin50=sinxcos40+cosxsin40
2cosxsin402sinxcos40=sinxcos40+cosxsin40
2cosxsin40cosxsin40=sinxcos40+2sinxcos40
tan40cosx=3sinx
so that
tanx=tan403

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?